Details

sample44.0ms

Algorithm

intervals

Results

7.0ms	185×	body	80	valid
6.0ms	34×	body	1280	valid
5.0ms	25×	body	2560	valid
4.0ms	115×	body	80	nan
3.0ms	9×	body	5120	valid
2.0ms	15×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	4×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.4b	(- (* b b) (* (* 4.0 a) c))
1.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

19.0ms	(* (* 4.0 a) c)
8.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series189.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (* 4.0 a) c)
42.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
59.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune391.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
0.6b	(cbrt c)
1.7b	(+ (- b) (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
24.7b	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def`
8×	`add-log-exp`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `distribute-rgt-neg-in` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`pow1/3` `sqrt-div` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 70

Calls

4 calls:

1.0ms	(cbrt c)
1.0ms	(cbrt c)
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
11.0ms	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series506.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt c)
172.0ms	(cbrt c)
86.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
82.0ms	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify39.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	276	645
1	1052	588
2	5001	574

prune274.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.2b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
53×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1/2`
15×	`swap-sqr`
10×	`fma-def`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3--` `flip--` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`rem-sqrt-square` `associate-r/` `associate-l/` `sum-log`
1×	`+-commutative` `pow2` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `pow-plus` `sqrt-unprod` `neg-log` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 144

Calls

4 calls:

61.0ms	(* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))
71.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
59.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
64.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	356	1458
1	1500	1280
2	5001	1245

prune435.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.1b

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
10.3b	(/ (+ 0 (* (* 4.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
117×	`*-un-lft-identity`
76×	`add-sqr-sqrt`
75×	`add-cube-cbrt`
45×	`associate-/l*`
40×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
21×	`distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r*`
10×	`neg-mul-1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `distribute-neg-frac` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-def` `sqrt-prod` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `sum-log` `flip--`

Counts

4 → 209

Calls

4 calls:

15.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
114.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
77.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
132.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
164.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
65.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify126.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	825	3590
1	3807	3333
2	5001	3330

prune604.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.6b

regimes217.0ms

Accuracy

92.6% (1.5b remaining)

Error of 12.2b against oracle of 10.7b and baseline of 31.5b

bsearch156.0ms

Steps

Iters	Range	Point
6	2.4781081934878466e+89	1.3380927769134863e+90	1.319255587955479e+90
6	-3.405927582379186e-150	-4.860750269204613e-151	-4.9276367402926466e-151
9	-8.193557888742793e+156	-5.650723842587128e+148	-1.3596472614638946e+154

Iters

Range

Point

2.4781081934878466e+89

1.3380927769134863e+90

1.319255587955479e+90

-3.405927582379186e-150

-4.860750269204613e-151

-4.9276367402926466e-151

-8.193557888742793e+156

-5.650723842587128e+148

-1.3596472614638946e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	40
1	61	40

end0.0ms

sample1.2s

Algorithm

intervals

Results

237.0ms	1059×	body	2560	valid
228.0ms	5787×	body	80	valid
167.0ms	896×	body	1280	valid
110.0ms	2934×	body	80	nan
70.0ms	490×	body	640	valid
40.0ms	114×	body	5120	valid
24.0ms	228×	body	320	valid
9.0ms	120×	body	160	valid